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<b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1"/><i><font color="Green" title="E10">A1</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="int_3.html#R1" title="INT_3:pred.1">&lt;=</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> )
 ;<br/><b>then consider </b><font color="Maroon" title="c4">a'</font>, <font color="Maroon" title="c5">b'</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E3:15_1"/><i><font color="Green" title="E11">A2</font></i>: 
( <font color="Maroon" title="c4">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c5">b'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c4">a'</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">b'</font> )
 <b>by </b><i><a class="ref" href="int_3.html#D4" target="_self" title="INT_3:def.4">Def4</a></i>;<br/><a NAME="E4:15_1"/>
for <font color="Olive" title="b1">b'</font>, <font color="Olive" title="b2">a'</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  holds <br/>(  not <font color="Olive" title="b1">b'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> or  not <font color="Olive" title="b2">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> or  not <font color="Olive" title="b1">b'</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">a'</font> )
 <b>by </b><i><a class="txt" href="int_3.html#E1:15_1"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="int_3.html#E3:15_1"><i><font color="Green" title="E11">A2</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/><b>hence </b><a NAME="E5:15_1"/>
<font color="Maroon" title="c2">a</font> <a href="int_3.html#NR3" title="INT_3:NR.3">&lt;</a> <font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="ref" href="int_3.html#D4" target="_self" title="INT_3:def.4">Def4</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:15"/>
( <font color="Maroon" title="c2">a</font> <a href="int_3.html#NR3" title="INT_3:NR.3">&lt;</a> <font color="Maroon" title="c3">b</font> iff ( <font color="Maroon" title="c2">a</font> <a href="int_3.html#R1" title="INT_3:pred.1">&lt;=</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> ) )
 ;<br/>


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